Ljubov Jaanuska doctoral thesis "Haar wavelet method for vibration analysis of beams and parameter quantification"

Klipi teostus: Merlin Pastak 19.02.2021 298 vaatamist Arvutiteadus


Juhendaja:
* külalisdots Helle Hein, TÜ arvutiteaduse instituut
 
 Oponendid:
 * prof Eduard Petlenkov, Tallinna Tehnikaülikool (Eesti);
 * kaasprof Jānis Šliseris, Riia Tehnikaülikool (Läti).
 
A beam is a common structural element designed to resist loading. Underestimated loads during the design stage, looseness during the manufacturing stage, corrosive environment, collisions, fatigue may introduce some damage to beams. If no action is taken, the damage can turn into a fault or a breakdown of the whole system. Hereof, the entirety of beams is a crucial issue. This dissertation proposes a systematic approach to vibration analysis and damage quantification in the Euler-Bernoulli type beams. The solution is sought on the modal properties such as natural frequencies and mode shapes. The forward problem of the vibration analysis is solved using the Haar wavelets and their integration since the corresponding differential equations do not have an analytical solution. Multiple numerical examples indicate that the proposed approach is fast and accurate. Damage quantification (location and severity) of a crack, a delamination, a point mass or changes in the stiffness coefficients of elastic supports on the bases of the modal properties is an inverse problem. Since it is not analytically possible to calculate the damage parameters from the vibration differential equation, the task is solved with the aid of artificial neural networks or random forests. The datasets are generated solving the vibration equations and decomposing the mode shapes into the Haar wavelet coefficients. Multiple numerical examples indicate that the Haar wavelet based dataset is calculated more than ten times faster than the frequency based dataset; the Haar wavelets are more sensitive to the damage location, while the frequencies are more sensitive to the damage severity; in most cases, the neural networks produce as precise predictions as the random forests. The results presented in this dissertation can help in understanding the behaviour of more complex structures under similar conditions, provide apparent influence on the design concepts of structures as well as enable new possibilities for operational and maintenance concepts.